Comparing Some Regions in a Square
In the figure below, quadrilateral
ABCD
is a square, and
E
is the midpoint of the side
AD
. How do the areas of regions I, II, III, and IV compare? Another way to think about this is to consider the question, What are the ratios of the areas of the

Problems

Suppose you love chocolate. The top of each cookie is covered with the same thickness of chocolate. If you wanted to choose the cookie with more chocolate, which would you pick?

Problems

Mara has 3 times as many dollars as her brother, Timmy. If Mara is given $20 by
their mother, she will have 7 times as many dollars as Timmy. How many dollars
does Timmy have?

Problems

Grades: 6th to 8th, 9th to 12th, 3rd to 5th

Ratio & Proportion

Functions

Algebra

Expression/Equation

Algebraic Thinking

Analyze proportional relationships and use them to solve real-world and mathematical problems.

Linear, Quadratic, and Exponential Models

Building Functions

Reasoning with Equations and Inequalities

Creating Equations

Use functions to model relationships between quantities.

Solve real-life and mathematical problems using numerical and algebraic expressions and equations.

Represent and analyze quantitative relationships between dependent and independent variables.

Reason about and solve one-variable equations and inequalities.

Multiply and divide within 100.

3.OA.C.7, 6.EE.B.6, 6.EE.C.9, 7.EE.B.4a, 8.F.B.4, HSA-CED.A.2, HSA-CED.A.3, HSA-REI.A.1, HSF-BF.A.1a, HSF-LE.A.2, 7.RP.A.2c

If each side of the triangle in Figure 1 is 1 inch long, this means the triangle has a perimeter of 3 inches. Suppose you continued the pattern in the diagram until you reached Figure 5. What is the sum of the perimeters of all the white triangles in Figure 5?

Problems

Grades: 9th to 12th, 3rd to 5th

Functions

Algebraic Thinking

Measurement & Data

Interpreting Functions

Generate and analyze patterns.

Geometric measurement: recognize perimeter as an attribute of plane figures and distinguish between linear and area measures.

Solve problems involving the four operations, and identify and explain patterns in arithmetic.

3.OA.D.9, 3.MD.D.8, 4.OA.C.5, HSF-IF.A.3

In the Sudoku grid at left, only the numbers along the perimeter are shown.

Suppose
the grid was completed according to the standard Sudoku rules — each row,
column and 3 × 3 square contains the numbers 1–9. Would the sum
of all the missing numbers be divisible by 3?

Problems